Single sideband system for digitally processing a given number of channel signals

ABSTRACT

A single sideband system for digitally processing a given number of analog channel signals, provided with: a digital filter to which filter coefficients are applied which characterized a lowpass filter having a cut-off frequency which is equal to half the bandwidth of the channel signals; a fast fourier transformer to which a number of carrier signal functions is applied, which number is at least equal to twice the number of channel signals and each of which represents a carrier frequency, each frequency being an even multiple of the cut-off frequency of the lowpass filter.

United States Patent Daguet et al.

[ 1 SINGLE SIDEBAND SYSTEM FOR DIGITALLY PROCESSING A GIVEN NUMBER OFCHANNEL SIGNALS [75] Inventors: Jacques Lucien Daguet, St. Maur;

Maurice Georges Bellanger, Antony; Guy Pierre Le'pagnol, Sceaux. all ofFrance [73] Assignee: Telecommunications Radioelectriques T.R.T., Paris,France [22] Filed: June 1, 1973 [21] Appl. No.: 366,073

[30] Foreign Application Priority Data June l5, I972 France 72.21646[52] US. Cl. 179/15 FS [5i] Int. Cl. H04j H18 [58] Field of Searchl79/I5 FS, l5 F0, 15 BC,

179]] SA, 15.55 R

[56] References Cited UNITED STATES PATENTS 3,573,380 4/l97l Darlington179/15 FS June 24, 1975 3,605,0l9 9/l97l Cutter r. l79/l5 FD 3,676.5987/l972 Kurthw. 3,808,4l2 4/l974 Smith l79/l5 BC OTHER PUBLICATIONS IEEESpectrum; Dec., 1967; "The Fast Fourier Transform" by Brigham et al..pp. 6370.

Primary Examiner-David L. Stewart Attorney, Agent, or FirmFrank R.Trifari; Henry I. Steckler [57] ABSTRACT 4 Claims, 9 Drawing FiguresPATENTEDJun 24 ms SHEET AF=NAf lll llallll PATENTEU Jun 2 4 I975 SI'iiEIIZTIZT 2T[ iiiiillilfli Fig.4

SHEET PATENTED JUN 2 4 I975 i-2N(P-2) N V V 2 I .IIIII z z \2 ,w w a n cv ll II AN 1 y m, b w hm 1| .1 2 2 3 3 (I. I I I .ll P g 5 P. 5 R 1 O 23 2, B B 8 0 Q I l l i II. II. 2 1/ X B a |+2N(P-1) Fig. 5

SINGLE SIDEBAND SYSTEM FOR DIGITALLY PROCESSING A GIVEN NUMBER OFCHANNEL SIGNALS The invention relates to a single sideband system fordigitally processing a given number of analog channel signals eachhaving a given bandwidth.

This digital processing may consist of, for example, the conversion of agiven number of base band signals (for example, speech signals in thefrequency band of -4 kHz) into a single sideband frequency divisionmultiplex signal. Alternatively, this digital processing may consist ofthe conversion of a given single sideband frequency division multiplexsignal into the original base band signals.

The single sideband systems suitable for the former digital processingmethod, referred to as single sideband frequency division multiplexsystems, and the single sideband systems suitable for the latter digitalprocessing method, referred to as a single sideband frequency divisiondemultiplex systems are, however, unequal in structure.

An object of the invention is to provide a single sideband system of thetype described above which is suitable for each of the twoabove-mentioned digital processing methods.

According to the invention this single sideband system includes an inputcircuit which is provided with a converter for sampling and convertingthe channel signals into a number of digital signals; a cascadearrangement of a fast fourier transformer and a digital filter, the saiddigital signals being applied to said cascade arrangement; a source fora given number of filter coefficients which are applied to said digitalfilter, said filter coefficients characterizing the transfer function ofa lowpass filter having a cut-off frequency which is equal to half thebandwidth of said channel signals; a source for a given number ofcarrier signal functions applied to said fast fourier transformer, saidnumber of carrier signal functions being at least equal to twice thenumber of channel signals, said carrier functions representing carrierfrequencies each being an even multiple of the cut-off frequency of thesaid lowpass filter.

The invention and its advantages will now be described in greater detailwith reference to the accompanying Figures.

FIG. I shows a single sideband system for converting a frequencydivision multiplex signal into the corresponding baseband channelsignals;

FIG. 2 shows, inter alia, a frequency diagram of the multiplex signal;

FIG. 3 shows the pulse response of a lowpass filter and series of signalsamples process by this response;

FIG. 4 shows with reference to series of samples the operation of aquadrature modulator shown in FIG. 1 and FIG. 5 shows a detailedembodiment of a calculator (or convolution means) according to FIG. 1and FIG. 6 shows its operation by means of a diagram,

FIG. 7 shows a single sideband system for converting a number ofbaseband channel signals into a frequency division multiplex signal andFIGS. 8 and 9 show transmission systems provided with a transmitter anda receiver each comprising a single sideband system according to theinvention.

FIG. I shows a single sideband system adapted for converting a frequencydivision multiplex of a number of single sideband-modulated channelsignals into the corresponding baseband channel signals. For example,this multiplex signal is located in the frequency band F -F of 312 to552 kHz and is formed by a secondary telephony group of 60 telephonychannels each having a bandwidth of O-Af, ie 4 kHz. This multiplexsignal whose frequency diagram is shown in FIG. 2a is applied in thesystem of FIG. 1 to the input terminal I of the input circuit Ia. Agroup of N channels with a bandwidth of AF= NAf in which N is preferablya number equal to an integral power of 2 is formed with idle channels atleast one of which adjoins the frequency F of the multiplex signal. Asis shown in FIG. 2a this group of N channels occupies the band AFbetween the frequencies F and F.,. In this Figure the channels are alsoenumerated 0 to N-l in the direction of the decreasing frequencies. Agroup of 64 channels 2 is formed with the said secondary telephony groupof 60 channels by introduction of four idle channels located on eitherside of the frequency band of 3l2-552 kHz and this group of 64 channelsoccupies the frequency band of F F i.e. 304-560 kHz.

This multiplex signal received through the input terminal I is appliedto the demodulator 2 so as to be demodulated with the aid of a carrierwhose frequency is in the center of the idle channel adjoining thehighest frequency F of the group of N channels. For the multiplex signalhaving the frequency diagram shown in FIG. 2a this demodulation carrierfrequency F. Afl2 is, for example, 558 kHz and is located in the centerof the channel no. 0. The output signal from the demodulator 2 isapplied to a lowpass filter 3 which eliminates the upper sideband of thedemodulated signal and from which a signal is derived whose frequencydiagram is shown in FIG. 2b. In this Figure the frequencies are given inthe form of the reciprocal of time. There applies that:

Also in the diagram of FIG. 2b the N channels are given and enumerated0-( N-l) in the direction of the increasing frequencies. The channel no.0 occupies in this case only the frequency band of [0 l/4T] Hz.

In an analog-to-digital converter 4 the signal coming from filter 3 issampled at a frequency 2F NIT and each sample is converted into a codeword of, for example, 12 binary elements (bits).

The series of coded samples is subsequently applied with a frequency ofN/T in the input circuit In to a series to parallel converter 5 whichprovides 2N interleaved series of samples which are applied to 2Nregisters r r r,- each having a storage capacity corresponding to onecode word. The contents of all registers are simultaneously applied, inthe rhythm of a read pulse signal L, at a frequency of l/2T to a digitalfilter constituted by 2N calculator members A,,, A A to which filtercoefficients originating from a memory 6 are applied, which filtercoefficients characterize a lowpass filter having a cut-off frequency ofl/4T. Sum signals each proportional to the sum of products of samplesand filter coefficients applied to these calculators (or convolutionmeans) A are generated by these calculators at a frequency of l/2T. Theoutputs 0 0' o-,-- of these calculators are applied to a transformer inthe form of a Fast Fourier transformer 7 to which carrier signalfunctions originating from a memory 6a are applied and which suppliestwo series of samples on each of its N independent pairs of output leadsP,,, P, P- said samples occurring at a frequency of l/ZT, one series ofsaid pairs of series corresponding to the phase component of the signalin a channel and the other series corresponding to the quadraturecomponent of the signal in the relevant channel. In order to obtain thecorresponding baseband channel signal from two of such series, theoutput leads are connected to a demodulator 3a and more particularlyeach pair of output leads P is connected to a quadrature demodulatord,,, d, deach supplying samples of a baseband channel signal at afrequency of UT.

Before describing the operation of the system according to FIG. I indetail, we still state which operations are to be performed so as toachieve the envisaged object.

In order to select in an ideal manner that portion of the total signallocated in the frequency band of O l/4T corresponding to the channel no.0, a lowpass filter is to be used with a cutoff frequency of l/4T and atransfer function of the shape as shown in FIG. 20. The frequencydiagram of the total signal is shown in FIG. 2b. As is khown the pulseresponse of such an ideal lowpass filter having this transfer functionhas a shape which is given by the function:

This function which is further shown in FIG. 3a has a maximum value atthe instant t= and is zero at the instant n.2T wherein n i1, 1 2. i 3

Non-recursive digital filtering means in this case convolving thesamples of the multiplex signal occurring at a frequency N/T with thepulse response of the filter. When the samples of the pulse response ofthe filter are denoted by a; at the instants when the samples S. of themultiplex signal occur, this filtering operation is based on thefollowing mathematical expression:

in which Q is an integer corresponding to the number of samples a of thepulse response, which samples will be referred to hereinafter as filtercoefficients.

This equation (I) may, however, be given in another form which can bederived from the series of samples of the multiplex signal shown in FIG.3b and from the pulse response shown in FIG. 3a of the digital lowpassfilter to be realized. This series of samples occurring at a frequencyNIT is limited to those samples which occur in a total time interval of2? time intervals 2T which are symmetrically distributed about the timet 0. The P X 2N samples located on the side of the positive time andcomprising the central sample S, are denoted by S wherein i= l, 2, 32N-l and thus characterizes each of the 2N samples within a timeinterval 2T. In this expression k assumes all integral values of 0 up toP1 inclusive and thus characterizes each of the P time intervals locatedon the side of the positive times. The P X 2N samples which are locatedon the side of the negative times are likewise denoted by S wherein k l,2. 3 P. In a corresponding manner the filter coefficients characterizingthe values of the pulse response at the instant of occurrence of thesamples of the multiplex signal may be represented by 0 By introducingthis manner of writing, equation (I) may be written as follows:

In order to select the multiplex signal shown in the frequency diagramof FIG. 2b that portion located in the frequency band of I/4T 3/4T andcorresponding to channel no. 1 a filter must be realized which has atransfer functioon of the shape as shown in FIG. 2d, i.e. a selectionfilter having a central frequency of l/2T and a bandwidth of l/2T. As isknown the transfer function of such a filter is the same as that of thelowpass filter of FIG. 2c but is subjected to a frequency shift off, 1/2T. As is known a frequency shift of f, of the transfer function of afilter is equivalent to a multiplication of the pulse response thereofby cos 211'l/4T for the phase component and by sin 21rt/4T for thequadrature component.

At the instant I i.2T/2N wherein i= 0, l, 2 2NI the phase and quadraturecomponents of the pulse response of the filter shown in FIG. 2d are thusrepresented by:

I m oes 2N and a sin 21. 2N

so that the phase component a of the output signal of the filter isgiven by:

Since in these expressions for the phase and quadrature components ofthe output signal of the filter the arguments of the goniometricfunctions due to the choice of the central frequency of the filter as aneven multiple of the cut-off frequency of the low-pass filter of FIG.20, are exclusively dependent on the variable i and independent of thevariable k, these expressions may be written as follows:

In order to determine simultaneously the phase and the quadraturecomponents of the signal, we will consider the following complex signal:

Analogously it can be shown that the signal in the H channel can beselected from the multiplex signal with a bandpass filter whose centralfrequency is n times the cut-off frequency l/ZT of the lowpass filteraccording to FIG. 2c. Accordingly the output signal C, of the filter forthis n" channel is given by:

And for the last channel no. N-l it is:

x-r untwast- For all these expressions (2). (3), (4) and (5) for Co, C iC C- the second summation is the same.

Writing:

The expressions for Co, C, i C C,, represent in the complex form thesignals in the channels 0, l ..n Nl and the coefficients C0, C, C, C maybe interpreted as the complex Fourier coefficients of the multiplexsignal. These coefficients Co, C C, C- have real parts a a, 01,, ozandimaginary parts 6,, B, B B in which the real part 3,, corresponds to thephase component of the signal in channel no. n, and the imaginary part[3,, corresponds to the quadrature component of the signal in thatchannel.

By introducing the function W exp [-jrr/N] the equation (7) may bewritten in a matrix form as follows:

In the system shown in FIG. 1 these complex Fourier coefficients C0, C Care calculated as follows: As already described the series-parallelconverter 5 provides 2N parallel series of samples which samples occurwithin each series at a frequency H21" and mutually exhibit a phaseshift of T/N. By indicating the samples of the multiplex signal of FIG.2b in the manner shown in FIG. 3b by S the samples which occur at agiven output of the converter 5 correspond to a given fixed value forthe variable i, but the samples occurring successively at this outputdiffer in the value of the variable index k.

For the purpose of illustration FIG. 3c shows the samples applied by theconverter 5 and corresponding to the fixed value for i namely i 0 wherek is chosen to be variable between -P and Pl.

FIG. 3d shows such a series of samples for a given 1' and for a kvariable between P and P-l that is to say, a series of samples suppliedby the output lead i of the converter 5.

These 2N series of samples stored in the register r,,r aresimultaneously applied to the 2N calculators A, of the digital lowpassfilter 2a. In these calculators the samples are multiplied in accordancewith expression (6) byfilter coefficients a for generating the sumsignal samples in defined by this expression (6).

'It is to be noted that the memory 6 in which all filter coefficientsaHzNk are stored in a so-called ROM memory, that is to say, a read-onlymemory from which the 2N coefficients are derived at a frequency l/2T.

It is also to be noted that in the described embodiment in which allcalculators operate simultaneously the same coefficients can be used indifferent calculators so that in practice the memory may have a smallercapacity than that which corresponds to 2NP coefficients.

The'signal sum samples 0' a. a are applied to the Fast Fouriertransformer 7 for carrying out the operation defined by equation (7) or(8) for determining the complex Fourier coefficients C C C Any FastFourier transformer commercially available may be used. The operation ofsuch a transformer is described, for example in an Article of Bellangerand Bonneval in lOnde Electrique, vol. 48, no. 500, November I968. Thistransformer provides the N complex Fourier coefficients for thedetermination of which only a minimum number of multiplications isrequired, which number is equal to 2N log N in the case where N is apower of 2. The coefficients cos wi/N used in the Fast Fouriertransformer may not only be provided by a separate memory 6a but also bythe coefficient memory 6 which comprises a large number of coefficientsfor use in combination with the the calculators with a value locatedbetween I and +1. The Fast Fourier transformer 7 provides at a frequencyI/ZT at its N independent pairs of output terminals P P, P samples ofthe complex Fourier coefficient C,,, C C,, The two output terminals ofeach pair, for example, the two terminals p, and p of the pair p,provide the samples of the real part a, and of the imaginary part Brespectively, of the complex coefficient C As already noted the samplesa constitute the phase component (1) of the signal in channel no. n andas is known this component may be written in the form of 4T +sq(l) cos(9) 2m 2m aqu) =3) sin T-sqfl) cos T (ID) The demodulators d0, d d whichare connected to the pairs of outputs of the transformer 7 then provide,with the aid of the signal components 01!) and (rq(r) the samples of theelementary signal s(t), which samples, according to Shannon, must occurat a frequency of UT. The equivalent analog method (method of Weaver),which makes it possible to obtain the elementary signal s(t) startingfrom the two components (1(1) and 0'q(t) consists in that each of thesecomponents is first filtered and subsequently demodulated with carriersignals mutually shifted 90 in phase; this means with cos 21rr/4T andsin 21'rt/4T, respectively, whereafter the two output signals arecombined.

The demodulators do, d dare then a digital translation of the knownanalog quadrature demodulator. In the digital embodiment in FIG. 1 ofthe quadrature demodulators one digital filter is used for which afilter of the non-recursive type may be chosen. The demodulation processwill be further described with reference to the demodulator a of FIG. 1and the diagrams of FIG. 4. In FIG. 4 a series of six samples a, isshown at a which samples occur with a period 2T and which are applied inthe demodulator to a delay circuit 8 shifting the series over a constanttime AT which is a multiple of 2T and thus provides the series ofsamples 01' shown in FIG. 4b. The sample series B likewise occurringwith a period 2T is shown in FIG. 4c. These samples are applied to adigital filter 9 of the nonrecursive type having a transfer function asshown in FIG. 2c. This filter 9 which thus has a cut-off frequency ofI/4T provides the series of samples 3' with a delay of AT as is shown inFIG. 4d. These samples are determined by the sum of products of thesamples [3,, and filter coefficients which indicate the values of thepulse response of the filter at instants which do not coincide with theinstants of occurrence of the samples [3,, but at instants which arelocated in the middle between two successive samples ,8, so that thusalso the samples B, occur in the middle between two successive samples[3 The filter coefficients for this filter may also be derived from thememory 6 which in fact comprises the coeffcients for the filter 2acharacterizing a low-pass filter having a cut-off frequency of l/4T.

The two series a' and 3' are subsequently applied to arrangements 10 and11, respectively, which reverses the sign of every second sample, whichin view of the fact that the two series oz' and 3' are mutually shiftedover a time T is the digital equivalent ofa modulation by two carriersmutually shifted in phase and each having a frequency of I/4T. In FIGS.4e and 4fthe two series obtained in this manner are shown. In theseFigures the and signs indicate the polarity of the relevant sample.These two series are subsequently combined in a combination device 12which provides the series of samples shown in FIG. 4g. Thus samples ofthe elementary signal 3(1) transported by channel no. n are obtained atthe output of the demodulator u: with a frequency of HT.

All quadrature demodulators shown in FIG. I are identical and operate inthe same manner. All of them simultaneously supply samples at afrequency of UT of the different elementary signals transported in thechannels. In the above-mentioned example, which relates to a frequencydivision multiplex of a group of 60 telephony signals, the samples ofthe 60 baseband signals fed back to the frequency band of 04000 Hzoccurring with the sampling frequency of 8000 Hz are obtained at theoutput of 60 demodulators.

FIG. 5 diagrammatically shows an embodiment of a calculator A, used inthe filter 2a supplying the samples a, which samples are determined inaccordance with equation (6) Le. using a series of 2P samples occurringat the output of the register r and 2? filter coefficients of a group of2 NP coefficients of a low-pass filter. In FIG. 3d this series of 2Psamples is shown in accordance with:

i-ZNIH i-eMP-o i wamp-2) SI+2N(PI)1 The filter coefficients are in thiscase also the values of the pulse response of FIG. 3a at the instantswhen these samples occur. These coefficients are indicated with the aidof the same index as that for the samples, for example, by:

A sample 0-, which is determined with the aid of these 2P input samplesand these 2? coefficients has the value O' (a.S) (a.S),- l" ((1.8%)|'+2N(P+2) )i+2N(PU (ll) In the circuit according to FIG. 5 the samplesare applied through an input terminal 13, a cascade arrangement of anAND-gate l7 and an OR-gate 16 to a shift register 14. The output of thisregister is connected to its input through an AND-gate I7 and theOR-gate 16. The gate 15 is enabled during the period determined by acontrol signal applied to an input terminal 18. By using an inverter 19the gate 17 is enabled in the absence of this control signal so that theregister 14 then operates as a dynamic memory. the AND-gate 17 isprovided with an input 23 through which it is possible to break down theword stores in the memory, which will be described hereinafter.

The output of register 14 is connected to a first input of 2P AND-gatesx x x each having a second input which is connected to the coefficientmemory 6 and to which the coefficients a; a, EH45]. are applied. Theoutput of each of these AND- gates is connected to an input of adder B,,B B the outputs of which are connected to inputs of 2P shift registers RR R respectively. The output of the register R is connected to a secondinput of the adder B through the AND-gate y and the outputs of theregisters R R R are connected to second inputs of the adders 8 I3 Bthrough AND-gates y y y and OR-gates 0 0 p, respectively. The AND-gatesy,, y: yzp are enabled in the absence of the control signal which isapplied to the input terminal 18. Finally the output of each of the 2Plfirst registers R R R is connected to the second input of the adders B BB through the AND-gates z 2 Z2p and the OR-gates 0 0 02p, respectively.The output of the last register R is connected through an AND-gate 1 tothe output terminal 20 of the calculator. The AND-gates z Z2 z areenabled during the period when the control signal applied to terminal 18is present.

The samples occurring with a period 2T which are applied via the inputterminal 13 to the calculator and are coded into PCM words eachcomprising a given number of bits (for example, 12) which are applied inseries and in the rhythm of a local clock pulse to this input 13, thebit having the slightest weight coming first. The 2P so-calledmultiplier registers R R R each include a number of D elements which islarger than the number of bits ofa sample. The register 14 includes anumber of D elements which is equal to D,l In a practical case thesevalues are, for example, D =20 and D IQ.

The operation of the circuit of FIG. is effected under the control ofthe control signal applied to terminal 18. This signal which has thesame period 2T as the samples is shown in FIG. 6a startingat the instantt when the first bit of the first sample S is applied to the input 13.During a first time interval (t when the control signal has a valuewhich will be indicated by l the gate 15 is enabled, the gate 17 isblocked and this bit of the sample S is introduced into the register 14in the rhythm of a local clock pulse. In the example chosen the interval(1 has 16 clock periods. At the instant I, the first bit appears, namelythat of the slightest weight of the total numer of D, 20 bits at theoutput of the register 14, which bit is subsequently applied to thefirst input of each of the AND-gates x,, x, .xzp.

At the instant t, the control signal assumes a value which will beindicated by 0. At this instant the gate 15 is blocked and the gate 17is enabled. The AND-gate is not only blocked by the control signal butalso by a .blocking signal occurring at its input 23 with a periodicityof D local clock pulses and every time it blocks lthis AND-gate 17 whenthe bit of the slightest weight occurs at the output of register 14.Thus from the instant l" to the instant 1 when again a l of the controlsignal occurs, the memory 14 operates as a dynamic memory in which foreach period equal to D local clock pulses the stored word is divided by2.

Since during this interval (r' t the gates z 2 z are blocked so that theoutputs of the registers R,, R R are not connected to the output 20while the gates y y: y are not blocked, the registers R,R operate asdynamic memories. During this time interval (t' t the multiplications ofthe sample S by the Coefficients l-21w i-i'NtP-l) i+2.VlP-l)1 are Pformed so that at the instant 1 a word is written in each register Il -Rconstituted by the sum of a word obtained by multiplication and a wordalready written in the register.

During this interval (t',, 1 the bits of the filter coefficients arederived from the memory 6 and are applied in series to the second inputof the gates x,, x x the bit of the highest weight coming first. Thenumber of bits of each coefficient is, for example, l2 and the durationof each bit is, for example, 20 local clock pulses which is equal to theduration of D clock periods of the registers R -Rzp. FIG. 6diagrammatically shows how in the register R the product ai 2 p. SPZNP(a.S), is realized. To this end FIG. 6 shows at b a series of 12 bits ee c of the coefficient a, which series is applied to the second input 21of the gate x During the time when the first bit e of, for example, thehighest weight is applied to this input 21 all bits of the sample Sappear at the first input 22 of the gate x and dependent on whether ehas the value I or 0 the sample (in word form) is written in or notwritten in register R The starting point in this case is that thisregister is empty at the commencement of the multiplication operation.In the period constituted by 20 clock periods during which the secondbit e of the filter coefficient is applied to the AND-gate x thisregister, with a view to the fact that the register 14 includes only l9elements, applies a binary word to the second input 22 of the gate x,which word corresponds to half the value of the latest considered sampleS Dependent on whether the bit e has the value 1 or O, the gate xapplies or does not apply this half sample value VzS to an input of theadder B to which the latest considered sample value S is applied throughthe other input, which value is written in R This adder B forms the sumof the two applied sample values 8,. and %S which sum is written in theregister R This process is subsequently repeated with the aid of theother bits of the filter coefficient 0 at which the value of the sampleis halved by shifting relative to the latest value used so that at theinstant t the complete product a, .S is written in the register R Inthis first interval (t' t the multiplication of the sample S[ 2Np by theother coefficients a p a; is simultaneously performed by using theregisters R R in the same manner while outputs of these registers areconnected to adders Bg-Bzp, the only difference being that theseregisters are generally not empty at the instant of commencement t, ofthe interval so that each register at the end of the interval retainsits initial contents at the instant I: with the addition of the resultof the multiplication. For determining the value of the sample 1', itis, however, sufficient to indicate the contents of the register R atthe instant I, of

this interval. These contents are shown in FIG. 6 on the line R by theindication aspe During the second I pulse of the control signal whichoccurs at the time interval t the second sample Si2N p is written inregister 14. In addition this 1 pulse blocks the gates y y y and itenables the gates 1., z 1 so that the contents of each of the registersR Rhd 2 R L in the interval t' are shifted to the respective registers RR R In FIG. 6 the shift of the contents (0.8),- from R to R is indicatedby a slanting arrow.

During the interval (r t the second sample S,- is multiplied by thefilter coefficients. For the register R: this means, for example. thatthe contents of this register at the end of this time interval areformed by the sum of the product (a.S),- shown in FIG. 6 on line R andthe product (a.S),- shifted in this register.

In the same manner the third sample S, is written in the register 14during the third I pulse occurring in the interval t';,) of the controlsignal and the con tents (a.S),- (a.S), are shifted from R, to registerR Subsequently the product (a.S),- is formed and added in the register Rto the initial contents.

The successive operations of this kind thus result in that the (2P)"' 1pulse of the control signal occurring in the time interval (1 r' writesthe contents )i2NP )i-2MP-i) hump-2 of the register R in the register Rand in the multiplication interval immediately following this intervalthe product (a.S) is added to the initial contents 0f R2).

The register Rap thus includes the sample 1'; represented by equation(11). This sample will be derived from the output of the calculatorunder the control of the 1 pulse of the control signal occurring duringthe interval (t t' The calculator shown in FIG. 5 is particularlysuitable for large scale integration in which this circuit may bemanufactured with MOs techniques and multiple logic. This circuitactually satisfied in an optimum manner all requirements which are to beimposed thereon in order to be formed in this technique. It includes,for example, a minimum number of connections because all operations areperformed on numbers with series bits; the multiplications are performedin series with only a limited number of elements and the required clockfrequency is relatively low.

In the example described above in which the registers R,-R,, comprise 20elements and the coefficients consist of 12 bits the time additionallyrequired for multiplying a sample by the filter coefficients is 12 X 20local clock periods. The time required for writing the sample in theinput register 14 is 16 local clock periods so that the time interval 2Tis to comprise a total of [2 X 20) [6 256 local clock periods. For abaseband channel signal having a bandwidth of Af of 4 kHz the interval2T is equal to 1/4000 second. For performing the multiplications a clockfrequency is required of 4 X 256 I024 kHz which is a value eminentlyadapted for realizing the calculator as an integrated MOS circuit.

FIG. 7 shows a single sideband system for converting N baseband channelsignals into a frequency division multiplex signal. To this end thissystem includes an input circuit 30a having N inputs leads i i ieach ofwhich is connected to an analog-to-digital converter E -E providing thecoded samples (PCM words) of a channel signal located in the frequencyband of (0 lY/ZT). The frequency at which the samples occur is chosen tobe equal to l/T in accordance with Shannon.

[11 this system the synchronously operated analog-todigital converters EE supply samples of the baseband channel signals coded with l2 bits.These channel signals are formed, for example, by telephony signals inthe frequency band of from 0 to 4000 Hz and are sampled in the converterE -E,,- at a frequency of 8000 Hz. For realizing a frequency divisionmultiplex signal in which only one modulation sideband occurs of allmodulated channel signals, the same digital operations as in the systemaccording to FIG. I are performed in this digital system, though inreverse order. More particularly the samples of the N baseband channelsignals are applied to N quadrature modulators M M M- performing thesame operations on the applied samples as the quadrature demodulators d,d d These operations are shown in FIG. 4 in which, however, the diagramsare to be read from g to a.

As is shown in greater detail for the modulator Mn to which the samples(FIG. 4g) ofa baseband channel signal s(r) are applied, each of thesemodulators has an inverter contact 25 at its input which supplies twointerleaved series of samples in each of which the samples occur at afrequency of l/ZT. In each of these series the sign of one of every twosamples is reversed with the aid of the circuits 26 and 27 (FIGS. 4e and4f) which is equivalent to modulating the signal s(t) with two mutuallyphase-shifted carriers cos 21rt/4T and sin 21rt/4T each having afrequency of I/4T (half the frequency band 0 l/2T of the signal s(r).Starting from the series of samples supplied by the circuit 27 thesamples which characterize the value of the information signal at theinstants located between two successive supplied samples are determinedwith the aid of the lowpass filter 29 which is chosen to be of thenonrecursive type having a cut-off frequency of l/4T and this bydetermining the sum of products ofa given number of samples and filtercoefficients characterizing the filter. Likewise as in FIG. 1 thesesamples are again obtained with a delay time AT. The delay circuit 28shifts with the same time AT the series of samples which are supplied bythe circuit 26. Thus two series of samples oz, and B are derived fromthe output of the modulator Mn which series represent the samples of thephase component 0*(t) and quadrature component a'q(t) of the signal inthe n" channel of the multiplex signal. These components 01 r) ando'q(r) are likewise given by the expressions (9) and (10). The seriesat, and [8,, may furthermore be considered as the real and imaginaryparts of the complex Fourier coefficient C,,*' of the signal which istransmitted in the channel no. n of the multiplex signal. Thiscoefficient may be written as C,. a,.+j,P of the interval having anlength of 2T and k passes through all integral values from to P-I.

With the same consideration as that corresponding to the systemaccording to FIG. 1 it is found that in a given time interval having alength of 2T (given value for k) each of the 2N samples of the multiplexsignal can be written as In this expression (12) 1 assumes all integralvalues from to 2N-l and likewise as in the foregoing a represents acoefficient of a lowpass filter having a cutoff frequency of 114T. Ofthis expression the second expression is firstly determined likewise asin the foregoing with the aid of a Fast Fourier transformer 30 whichstarting from N complex Fourier coefficients C C C C determines 2Ncomplex numbers of which exclusively the real parts a a," a a areutilized for the further operations.

By writing W= exp [jvr/N] the operation to be performed can in matrixform be expressed as follows:

(7 l l l l (7 l W W W real 0'," part I W' W" W k MN-I uuv-n mi "av-nStarting from 2P real numbers a, the 2N samples S are subsequentlydetermined which occur in a time interval 2T. It follows from theexpression (I2) that these samples 5, may be written as:

On the one hand the complex Fourier coefficients C,,", C, C- occurringat the frequency of l/2T at the outputs of the modulators M M- areapplied to the Fast Fourier transformer 30 shown in FIG. 7 and on theother hand carrier signal functions W originating from a memory 31a areapplied to this Fast Fourier transformer wherein r I, I, (N1)(2NI). TheFast Fourier transformer 30 performs the operations defined by equationsl3) and provides through its 2N output leads 2N series of real numbers 00' a which numbers occur with the frequency of l/ZT at each of theoutput leads. These 2N series are subsequently applied to a lowpassfilter 32a which is constituted by 2N calculators H H H to which one ofthe series o and in addition filter coefficients a originating from amemory 31 are applied. In these calculators the numbers 0- 0-,", o'- aremultipled by filter coefficients 0 in accordance with expression 14).These calculators which together constitute a lowpass filter having acut-off frequency of l/4T may be formed in the same manner as those inFIG. 1 and a detailed embodiment of these calculators is shown in FIG.5.

Likewise as in the system of FIG. 1 the coefficients from the memory 31may also be used for the operations to be performed in the circuit 30and for the lowpass filters 29 in the modulators M,,M

In the described system the 2N calculators H,,H supply 2N simultaneousseries of samples For interleaving these series the output of each ofthe calculators Fl -H is connected in the output circuit 33a to aregister r r r each having a capacity corresponding to the number ofbits of the sample at the output of the calculator. The samples in theregisters r,,, r r e, are successively applied to the common output lead32 through AND-gates h h h with the aid of read pulse signals L L li e,which mutually have a time shift of T/N and which each occur at afrequency of l/2T.

For the samples of a frequency division multiplex signal located in thefrequency band [0 N/ZT] occur in this common lead 32 at a frequency ofN/T. In order to obtain this signal, whose frequency diagram is shown inFIG. 2b, in an analog form these samples are applied to thedigital-to-analog converter 33 which converts the incoming words intoamplitude-modulated pulses which are applied to the bandpass filter 34supplying an analog signal having a frequency diagram according to FIG.2b. The desired location of the frequency division multiplex signal isobtained with the aid of a modulator 35 to which a carrier signal of thefrequency F Af/2 wherein (Af= l/2T) is applied. The frequency divisionmultiplex signal is thus transposed in frequency to a frequency band F Fhaving a width of NAf. FIG. 2a shows this transposition in a diagram.

FIGS. 8 and 9 show some important possibilities of use of the systemsaccording to the invention. The transmission system shown in FIG. 8 forfrequency division multiplex signals is provided with a transmitter 40and a receiver 41 which are connected together, for example, through acoaxial cable. In the transmitter 40 which is built up in the manner asis shown in FIG. 7 a number of baseband channel signals, for example,speech signals is converted into a frequency division multiplex signalwhich is transmitted through the transmission lead to the receiver 41build up in the manner as is shown in FIG. 1 and in which the receivedmultiplex signal is converted into the original baseband channelsignals.

FIG. 9 shows an intermediate station 40,41 establishing a connectionbetween a single sideband frequency division multiplex transmissionsystem and a time division multiplex transmission system. Moreparticularly the frequency division multiplex signals which aretransmitted by a terminal station 50 of the frequency division multiplextransmission system are applied to a single sideband system 41 which isbuilt up in the manner as is shown in FIG. 1 and are converted in thissystem into a number of baseband channel signal samples which arecombined in an arrangement 52 and are subsequently transmitted through atransmission lead to a terminal station 51 of a time division multiplextransmission system. Conversely, the time division multiplex signalstransmitted by the terminal station 51 are applied through atransmission lead to a single sideband system 40 which is built up inthe manner as is shown in FIG. 7 where the samples of baseband signalstransmitted in time division multiplex are applied through aseries-parallel converter to the system 40 for conversion of thesebaseband channel signals into a frequency division multiplex signalwhich is transmitted through a transmission line to the terminal station50 of the single sideband frequency division multiplex transmissionsystem.

What is claimed is:

l. A single sideband system for digitally processing a given number ofanalog channel signals each having a given bandwidth, said systemcomprising an input circuit including a converter means for sampling andconverting the channel signals into a number of digital signals; acascade arrangement coupled to said input circuit and including a FastFourier transformer means and a digital filter coupled to saidtransformer means, said digital signals being applied to said cascadearrangement; a source for generating signals representative of a givennumber of filter coefficients coupled to said digital filter, saidfilter coefficients characterizing the transfer function of a lowpassfilter having a cut-off frequency which is equal to half the bandwidthof said channel signals; a source for a given number of carrier signalfunctions coupled to said transformer means, said number of carriersignal functions being at least equal to twice the number of channelsignals, said carrier functions representing carrying frequencies eachbeing an even multiple of the cut-off frequency of said lowpass filtersaid analog channel signals comprising a given number of basebandchannel signals, said input circuit including a number of parallelsignal channels,

said number corresponding to the number of baseband signal channels,each of said channels including a converter means for sampling eachbaseband channel signal with the associated Nyquist frequency, saidsignal channels each including a modulator coupled to said convertermeans, the transformer means having inputs coupled to said modulatorsfor generating a number of first sum signals each being proportional tothe sum of products of output signals from said modulator and carriersignal functions, said transformer means having a number of output leadswhich number is equal to the number of first sum signals, said outputleads being coupled to the digital filter, said filter having a numberof signal channels said number corresponding to the number of outputleads, each signal channel being coupled to the number of output leadsand each including a convolution means coupled to said filtercoefficient source for generating a second sum signal which isproportional to the sum of products of first sum signals and filtercoefficients applied to said convolution means, means for applying saidsecond sum signals in the rhythm of successively occurring read signalsto a common output lead for generating a frequency division multiplexsignal in an auxiliary frequency band, an output circuit, means forapplying said multiplex signal to said output circuit, said outputcircuit comprising a digital-to-analog converter and a second modulatormeans coupled to said digital to analog converter for transposing saidfrequency division multiplex signal from the auxiliary frequency band tosaid given frequency band.

2. A single sideband system as claimed in claim 1, wherein the modulatorin the input circuit comprises a number of quadrature modulators each ofwhich is incorporated in a signal channel, said quadrature modulatorseach including means for providing two phase shifted carrier-modulatedchannel signals, the transformer means comprising a number of inputmeans coupled to said quadrature modulators equal to an integral powerof two and a number of output leads corre sponding to this number.

3. A single sideband system for digitally processing a given number ofanalog channel signals each having a given bandwidth, said systemcomprising an input circuit including a converter means for sampling andconverting the channel signals into a number of digital signals; acascade arrangement coupled to said input circuit and including a FastFourier transformer means and a digital filter coupled to saidtransformer means, said digital signals being applied to said cascadearrangement; a source for generating signals representative of a givennumber of filter coefficients coupled to said digital filter, saidfilter coefficients characterizing the transfer function of a lowpassfilter having a cut-off frequency which is equal to half the bandwidthof said channel signals; a source for a given number of carrier signalsfunctions coupled to said transformer means, said number of carriersignals functions being at least equal to twice the number of channelsignals, said carrier functions representing carrying frequencies eachbeing an even multiple of the cutoff frequency of said lowpass filtersaid analog channel signals comprising a single sideband frequencydivision multiplex signal lo cated in a given frequency band, said inputcircuit including a modulator having a first input means for receivingfrequency division multiplex signal, a second input means for receivinga carrier signal, and an output means for providing a frequency divisionmultiplex signal whose lowest frequency corresponds to an odd multipleof the cut-off frequency of said lowpass filter, the converter meanssampling at a frequency which is equal to the Nyquist frequency of saidsignal and having an input coupled to said modulator output and anoutput, said input circuit furthermore including a series-to-parallelconverter comprising an input coupled to said converter means output anda given number of output leads which number is equal to the ratiobetween said Nyquist frequency and the bandwidth of a baseband channelsignal; said digital filter in said single sideband system including anumber of parallel signal channels each being coupled to an output leadof the series-to-parallel converter and each including a convolutionmeans coupled to said filter coefficient source for generating a firstsum signal which is proportional to the sum of the products of signalsand filter coefficients applied to said arrangement and having anoutput, said transformer means being coupled to said convolution meansoutput for generating a number of second sum signals each beingproportional to the sum of products of said first sum signals andcarrier signal functions, an output circuit including a demodulatormeans coupled to said transformer means for demodulating said second sumsignals and for generating baseband signals each corresponding to asignal in a given frequency band of the frequency division multiplexsignal.

4. A single sideband system as claimed in claim 3, wherein the number ofoutput leads of the series parallel converter is an integral power oftwo and that the Fast Fourier Transformer has a number of pairs ofoutput leads corresponding to the number of channel signals, the outputleads of each pair comprising means for providing phase-shiftedmodulated signals, each pair of output leads being connected to thedemodulator, the demodulator in said single sideband system comprising anumber of quadrature demodulators, said number corresponding to saidnumber of pairs of output leads, an input circuit of each of saidquadrature demodulators being coupled to one of said pairs of outputleads.

1. A single sideband system for digitally processing a given number of analog channel signals each having a given bandwidth, said system comprising an input circuit including a converter means for sampling and converting the channel signals into a number of digital signals; a cascade arrangement coupled to said input circuit and including a Fast Fourier transformer means and a digital filter coupled to said transformer means, said digital signals being applied to said cascade arrangement; a source for generating signals representative of a given number of filter coefficients coupled to said digital filter, said filter coefficients characterizing the transfer function of a lowpass filter having a cut-off frequency which is equal to half the bandwidth of said channel signals; a source for a given number of carrier signal functiOns coupled to said transformer means, said number of carrier signal functions being at least equal to twice the number of channel signals, said carrier functions representing carrying frequencies each being an even multiple of the cut-off frequency of said lowpass filter said analog channel signals comprising a given number of baseband channel signals, said input circuit including a number of parallel signal channels, said number corresponding to the number of baseband signal channels, each of said channels including a converter means for sampling each baseband channel signal with the associated Nyquist frequency, said signal channels each including a modulator coupled to said converter means, the transformer means having inputs coupled to said modulators for generating a number of first sum signals each being proportional to the sum of products of output signals from said modulator and carrier signal functions, said transformer means having a number of output leads which number is equal to the number of first sum signals, said output leads being coupled to the digital filter, said filter having a number of signal channels said number corresponding to the number of output leads, each signal channel being coupled to the number of output leads and each including a convolution means coupled to said filter coefficient source for generating a second sum signal which is proportional to the sum of products of first sum signals and filter coefficients applied to said convolution means, means for applying said second sum signals in the rhythm of successively occurring read signals to a common output lead for generating a frequency division multiplex signal in an auxiliary frequency band, an output circuit, means for applying said multiplex signal to said output circuit, said output circuit comprising a digital-to-analog converter and a second modulator means coupled to said digital to analog converter for transposing said frequency division multiplex signal from the auxiliary frequency band to said given frequency band.
 2. A single sideband system as claimed in claim 1, wherein the modulator in the input circuit comprises a number of quadrature modulators each of which is incorporated in a signal channel, said quadrature modulators each including means for providing two phase-shifted carrier-modulated channel signals, the transformer means comprising a number of input means coupled to said quadrature modulators equal to an integral power of two and a number of output leads corresponding to this number.
 3. A single sideband system for digitally processing a given number of analog channel signals each having a given bandwidth, said system comprising an input circuit including a converter means for sampling and converting the channel signals into a number of digital signals; a cascade arrangement coupled to said input circuit and including a Fast Fourier transformer means and a digital filter coupled to said transformer means, said digital signals being applied to said cascade arrangement; a source for generating signals representative of a given number of filter coefficients coupled to said digital filter, said filter coefficients characterizing the transfer function of a lowpass filter having a cut-off frequency which is equal to half the bandwidth of said channel signals; a source for a given number of carrier signals functions coupled to said transformer means, said number of carrier signals functions being at least equal to twice the number of channel signals, said carrier functions representing carrying frequencies each being an even multiple of the cut-off frequency of said lowpass filter said analog channel signals comprising a single-sideband frequency division multiplex signal located in a given frequency band, said input circuit including a modulator having a first input means for receiving frequency division multiplex signal, a second input means for receiving a carrier signal, and an output means for providing a frequency division multiplex signal whose lowest frequenCy corresponds to an odd multiple of the cut-off frequency of said lowpass filter, the converter means sampling at a frequency which is equal to the Nyquist frequency of said signal and having an input coupled to said modulator output and an output, said input circuit furthermore including a series-to-parallel converter comprising an input coupled to said converter means output and a given number of output leads which number is equal to the ratio between said Nyquist frequency and the bandwidth of a baseband channel signal; said digital filter in said single sideband system including a number of parallel signal channels each being coupled to an output lead of the series-to-parallel converter and each including a convolution means coupled to said filter coefficient source for generating a first sum signal which is proportional to the sum of the products of signals and filter coefficients applied to said arrangement and having an output, said transformer means being coupled to said convolution means output for generating a number of second sum signals each being proportional to the sum of products of said first sum signals and carrier signal functions, an output circuit including a demodulator means coupled to said transformer means for demodulating said second sum signals and for generating baseband signals each corresponding to a signal in a given frequency band of the frequency division multiplex signal.
 4. A single sideband system as claimed in claim 3, wherein the number of output leads of the series parallel converter is an integral power of two and that the Fast Fourier Transformer has a number of pairs of output leads corresponding to the number of channel signals, the output leads of each pair comprising means for providing phase-shifted modulated signals, each pair of output leads being connected to the demodulator, the demodulator in said single sideband system comprising a number of quadrature demodulators, said number corresponding to said number of pairs of output leads, an input circuit of each of said quadrature demodulators being coupled to one of said pairs of output leads. 